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This study proposes and demonstrates how computer‐aided methods can be used to extend qualitative data analysis by quantifying qualitative data, and then through exploration, categorization, grouping, and validation. Computer‐aided approaches to inquiry have gained important ground in educational research, mostly through data analytics and large data set processing. We argue that qualitative data analysis methods can also be supported and extended by computer‐aided methods. In particular, we posit that computing capacities rationally applied can expand the innate human ability to recognize patterns and group qualitative information based on similarities. We propose a principled approach to using machine learning in qualitative education research based on the three interrelated elements of the assessment triangle: cognition, observation, and interpretation. Through the lens of the assessment triangle, the study presents three examples of qualitative studies in engineering education that have used computer‐aided methods for visualization and grouping. The first study focuses on characterizing students' written explanations of programming code, using tile plots and hierarchical clustering with binary distances to identify the different approaches that students used to self‐explain. The second study looks into students' modeling and simulation process and elicits the types of knowledge that they used in each step through a think‐aloud protocol. For this purpose, we used a bubble plot and a k‐means clustering algorithm. The third and final study explores engineering faculty's conceptions of teaching, using data from semi‐structured interviews. We grouped these conceptions based on coding similarities, using Jaccard's similarity coefficient, and visualized them using a treemap. We conclude this manuscript by discussing some implications for engineering education qualitative research. 

The mutual interactions between the synthetic gene circuits and the host growth could cause unexpected outcomes in the dynamical behaviors of the circuits. However, how the steady states and the stabilities of the gene circuits are affected by host cell growth is not fully understood. Here, we developed a mathematical model for nonlinear growth feedback based on published experimental data. The model analysis predicts that growth feedback could significantly change the qualitative states of the system. Bistability could emerge in a circuit without positive feedback, and high-order multistability (three or more steady states) arises in the self-activation and toggle switch circuits. Our results provide insight into the potential effects of ultrasensitive growth feedback on the emergence of qualitative states in synthetic circuits and the corresponding underlying mechanism. 

The Hippo-YAP/TAZ signaling pathway plays a critical role in tissue homeostasis, tumorigenesis, and degeneration disorders. The regulation of YAP/TAZ levels is controlled by a complex regulatory network, where several feedback loops have been identified. However, it remains elusive how these feedback loops contain the YAP/TAZ levels and maintain the system in a healthy physiological state or trap the system in pathological conditions. Here, a mathematical model was developed to represent the YAP/TAZ regulatory network. Through theoretical analyses, three distinct states that designate the one physiological and two pathological outcomes were found. The transition from the physiological state to the two pathological states is mechanistically controlled by coupled bidirectional bistable switches, which are robust to parametric variation and stochastic fluctuations at the molecular level. This work provides a mechanistic understanding of the regulation and dysregulation of YAP/TAZ levels in tissue state transitions. 

Abstract Failure of modularity remains a significant challenge for assembling synthetic gene circuits with tested modules as they often do not function as expected. Competition over shared limited gene expression resources is a crucial underlying reason. It was reported that resource competition makes two seemingly separate genes connect in a graded linear manner. Here we unveil nonlinear resource competition within synthetic gene circuits. We first build a synthetic cascading bistable switches (Syn-CBS) circuit in a single strain with two coupled self-activation modules to achieve two successive cell fate transitions. Interestingly, we find that the in vivo transition path was redirected as the activation of one switch always prevails against the other, contrary to the theoretically expected coactivation. This qualitatively different type of resource competition between the two modules follows a ‘winner-takes-all’ rule, where the winner is determined by the relative connection strength between the modules. To decouple the resource competition, we construct a two-strain circuit, which achieves successive activation and stable coactivation of the two switches. These results illustrate that a highly nonlinear hidden interaction between the circuit modules due to resource competition may cause counterintuitive consequences on circuit functions, which can be controlled with a division of labor strategy. 

Growth-mediated feedback between synthetic gene circuits and host organisms leads to diverse emerged behaviors, including growth bistability and enhanced ultrasensitivity. However, the range of possible impacts of growth feedback on gene circuits remains underexplored. Here we mathematically and experimentally demonstrated that growth feedback affects the functions of memory circuits in a network topology-dependent way. Specifically, the memory of the self-activation switch is quickly lost due to the growth-mediated dilution of the circuit products. Decoupling of growth feedback reveals its memory, manifested by its hysteresis property across a broad range of inducer concentration. On the contrary, the toggle switch is more refractory to growth-mediated dilution and can retrieve its memory after the fast-growth phase. The underlying principle lies in the different dependence of active and repressive regulations in these circuits on the growth-mediated dilution. Our results unveil the topology-dependent mechanism on how growth-mediated feedback influences the behaviors of gene circuits.